Learning Algorithm Evaluation

Algorithm evaluation: Outline Why? Overfitting How? Train/Test vs Cross-validation What? Evaluation measures Who wins? Statistical significance

Introduction

Introduction A model should perform well on unseen data drawn from the same distribution

Classification accuracy performance measure Success: instance’s class is predicted correctly Error: instance’s class is predicted incorrectly Error rate: #errors/#instances Accuracy: #successes/#instances Quiz 50 examples, 10 classified incorrectly Accuracy? Error rate?

Evaluation Rule #1 Never evaluate on training data!

Train and Test Step 1: Randomly split data into training and test set (e.g. 2/3-1/3) a.k.a. holdout set

Train and Test Step 2: Train model on training data

Train and Test Step 3: Evaluate model on test data

Train and Test Quiz: Can I retry with other parameter settings?

Evaluation Rule #1 Rule #2 Never evaluate on training data! Never train on test data! (that includes parameter setting or feature selection)

Train and Test Step 4: Optimize parameters on separate validation set testing

Test data leakage Never use test data to create the classifier Can be tricky: e.g. social network Proper procedure uses three sets training set: train models validation set: optimize algorithm parameters test set: evaluate final model

Making the most of the data Once evaluation is complete, all the data can be used to build the final classifier Trade-off: performance  evaluation accuracy More training data, better model (but returns diminish) More test data, more accurate error estimate

Train and Test Step 5: Build final model on ALL data (more data, better model)

Cross-Validation

k-fold Cross-validation Split data (stratified) in k-folds Use (k-1) for training, 1 for testing Repeat k times Average results train test Original Fold 1 Fold 2 Fold 3

Cross-validation Standard method: 10? Enough to reduce sampling bias Stratified ten-fold cross-validation 10? Enough to reduce sampling bias Experimentally determined

Leave-One-Out Cross-validation 100 Original Fold 1 Fold 100 ……… A particular form of cross-validation: #folds = #instances n instances, build classifier n times Makes best use of the data, no sampling bias Computationally expensive

ROC Analysis

ROC Analysis Stands for “Receiver Operating Characteristic” From signal processing: tradeoff between hit rate and false alarm rate over noisy channel Compute FPR, TPR and plot them in ROC space Every classifier is a point in ROC space For probabilistic algorithms Collect many points by varying prediction threshold Or, make cost sensitive and vary costs (see below)

TPrate (sensitivity): Confusion Matrix actual + - TP FP + true positive false positive predicted FN TN - false negative true negative TP+FN FP+TN P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity TPrate (sensitivity): FPrate (fall-out):

ROC space classifiers J48 parameters fitted J48 OneR P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity

ROC curves Area Under Curve (AUC) =0.75 Change prediction threshold: Threshold t: (P(+) > t) P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity Area Under Curve (AUC) =0.75

ROC curves Alternative method (easier, but less intuitive) Rank probabilities Start curve in (0,0), move down probability list If positive, move up. If negative, move right Jagged curve—one set of test data Smooth curve—use cross-validation

ROC curves Method selection Overall: use method with largest Area Under ROC curve (AUROC) If you aim to cover just 40% of true positives in a sample: use method A Large sample: use method B In between: choose between A and B with appropriate probabilities

ROC Space and Costs equal costs skewed costs P(TP): % true positives: sensitivity P(FP): % false positives: 1 – specificity

Different Costs In practice, TP and FN errors incur different costs Examples: Medical diagnostic tests: does X have leukemia? Loan decisions: approve mortgage for X? Promotional mailing: will X buy the product? Add cost matrix to evaluation that weighs TP,FP,... pred + pred - actual + cTP = 0 cFN = 1 actual - cFP = 1 cTN = 0

Statistical Significance

Comparing data mining schemes Which of two learning algorithms performs better? Note: this is domain dependent! Obvious way: compare 10-fold CV estimates Problem: variance in estimate Variance can be reduced using repeated CV However, we still don’t know whether results are reliable

Significance tests Significance tests tell us how confident we can be that there really is a difference Null hypothesis: there is no “real” difference Alternative hypothesis: there is a difference A significance test measures how much evidence there is in favor of rejecting the null hypothesis E.g. 10 cross-validation scores: B better than A? mean A mean B P(perf) Algorithm A Algorithm B perf x x x xxxxx x x x x x xxxx x x x

32 Paired t-test P(perf) Algorithm A Algorithm B perf Student’s t-test tells whether the means of two samples (e.g., 10 cross-validation scores) are significantly different Use a paired t-test when individual samples are paired i.e., they use the same randomization Same CV folds are used for both algorithms William Gosset Born: 1876 in Canterbury; Died: 1937 in Beaconsfield, England Worked as chemist in the Guinness brewery in Dublin in 1899. Invented the t-test to handle small samples for quality control in brewing. Wrote under the name "Student".

Performing the test Fix a significance level  P(perf) Algoritme A Algoritme B Fix a significance level  Significant difference at % level implies (100-)% chance that there really is a difference Scientific work: 5% or smaller (>95% certainty) Divide  by two (two-tailed test) Look up the z-value corresponding to /2: If t  –z or t  z: difference is significant null hypothesis can be rejected perf α z 0.1% 4.3 0.5% 3.25 1% 2.82 5% 1.83 10% 1.38 20% 0.88